• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.633-641
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• 1996

Let $P_J$ be a standard parabolic subgroup of a Chevalley group G and $U_J$ the unipotent radical of $P_J$. In this paper, we find a certain partition of the set of roots corresponding to root subgroups generating $U_J$ and investigate some properties of the partition.

• Communications of the Korean Mathematical Society
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• v.7 no.1
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• pp.41-48
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• 1992

• Communications of the Korean Mathematical Society
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• v.8 no.2
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• pp.213-223
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• 1993

• Kyungpook Mathematical Journal
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• v.16 no.1
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• pp.53-59
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• 1976

• Kyungpook Mathematical Journal
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• v.21 no.1
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• pp.63-69
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• 1981

• Honam Mathematical Journal
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• v.14 no.1
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• pp.25-35
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• 1992

• Communications of the Korean Mathematical Society
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• v.6 no.2
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• pp.261-266
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• 1991

• Honam Mathematical Journal
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• v.9 no.1
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• pp.7-17
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• 1987

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.635-653
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• 2005

We study the distribution of a dense orbit of a lattice A acting by the right multiplication on the space $\Gamma/G$ where G is a connected simple Lie group and $\Gamma$ its lattice. We show that for $G=SL_n(\mathbb{R})$, every dense orbit is equidistributed with respect to the Euclidean norm.

• Molecules and Cells
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• v.41 no.7
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• pp.631-638
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• 2018

Spermatogonial stem cells (SSCs) derived from mouse testis are unipotent in regard of spermatogenesis. Our previous study demonstrated that SSCs can be fully reprogrammed into pluripotent stem cells, so called germline-derived pluripotent stem cells (gPS cells), on feeder cells (mouse embryonic fibroblasts), which supports SSC proliferation and induction of pluripotency. Because of an uncontrollable microenvironment caused by interactions with feeder cells, feeder-based SSC reprogramming is not suitable for elucidation of the self-reprogramming mechanism by which SSCs are converted into pluripotent stem cells. Recently, we have established a Matrigel-based SSC expansion culture system that allows longterm SSC proliferation without mouse embryonic fibroblast support. In this study, we developed a new feeder-free SSC self-reprogramming protocol based on the Matrigel-based culture system. The gPS cells generated using a feeder-free reprogramming system showed pluripotency at the molecular and cellular levels. The differentiation potential of gPS cells was confirmed in vitro and in vivo. Our study shows for the first time that the induction of SSC pluripotency can be achieved without feeder cells. The newly developed feeder-free self-reprogramming system could be a useful tool to reveal the mechanism by which unipotent cells are self-reprogrammed into pluripotent stem cells.